A shortfall modelling-based solution approach for stochastic cyclic inventory routing

In today's business landscape, demand variability plays a crucial role in determining the success of companies across various industries. This article explores the concept of demand variability, encompassing both deterministic and stochastic demand patterns. We delve into the differences between these demand types and their implications for businesses. The article emphasizes the significance of accurate demand forecasting and its role in strategic decision-making. Deterministic demand, characterized by predictable patterns, allows businesses to forecast with certainty. On the other hand, stochastic demand introduces uncertainty, requiring statistical methods and probability theory for estimation and management. Furthermore, we explore the distinction between stochastic stationary demand and stochastic nonstationary demand. While the former maintains consistent statistical properties over time, the latter experiences fluctuations in its characteristics due to external factors. We highlight the challenges faced by businesses in forecasting and managing nonstationary demand and the need for adaptive forecasting methods. To successfully navigate today's dynamic market, companies must embrace advanced analytics and data-driven approaches. By leveraging historical data, statistical models, and forecasting techniques, businesses can gain valuable insights into demand patterns, optimize inventory management, and make informed strategic decisions. Ultimately, understanding and managing demand variability is paramount for businesses seeking to improve customer satisfaction, optimize operations, and enhance their competitive advantage. This article aims to provide a comprehensive understanding of demand variability and equip readers with insights and strategies to tackle the challenges posed by an ever-changing market landscape.

The inventory model for deteriorating items with a stochastic demand rate is studied in our paper. Inventory models dealing with the deterioration of items have attracted considerable interests in recent decades since the deteriorating phenomenon is a crucial factor affecting the profits of a company. However, most of current inventory models considering deterioration assumes a certain or a constant demand function which is unreasonable in the prevailing market that conforms to our daily reality. Therefore, stochastic demand must be considered. Besides, shortage is allowed in the study. We provide approximating solutions for optimal ordering quantities for our model, and show that our optimal solutions from the assumed models give conditions and results very close to the optimal solutions obtained by computation. Further, these results illustrate the impact of various parameters on the optimal policy and the profit.KeywordsEOQ modelDeteriorating EOQ modelStochastic demand

Inventory issues are often a major concern as they significantly impact operating costs. Lot sizing is one of the key decisions in managing inventory. However, in a real context, the demand for each item is often uncertain. It is supplied from the same supplier, requiring product orders to be placed in the same period. In addition, limited vehicle capacity and transportation costs are important factors to consider in making multi-item lot sizing decisions. The purpose of this study is to propose a new inventory model multi-item lot sizing model involving transportation cost and capacity constraints under stochastic demand. The decision variables involved in the model are each item's ordering cycle and safety factor with the objective function of minimizing the total inventory cost. To optimize the inventory model, this study also offers the advanced procedure of the Aquila Algorithm. This study also presents sensitivity analysis to the appropriate policy for optimizing the multi-item lot-sizing inventory problem involving transportation cost and capacity constraint under stochastic demand.

This paper studies the reference effect on dynamic pricing in revenue management for cases with limited capacity and stochastic demand. We first present a single‐period fixed pricing (FP) model in finite horizon with fixed capacity and stochastic demand, and show that there is a unique optimal solution. The model is then extended to a discrete‐time dynamic pricing (DP) model as a benchmark case. We subsequently propose a DP model with reference effect (DPR), investigate the properties of the revenue function, and present a computational scheme to compute the dynamic optimal price. Numerical experiments are conducted to exhibit how the reference effect may influence the initial price, pricing trend, price dispersion, and expected revenue, with the FP, DP, and DPR policies in the same environment of a fixed capacity facing stochastic demand. We also present, through numerical examples, a comparison between deterministic demand and stochastic demand scenarios under reference effect, and with a fixed initial price versus a variable initial price.

We model supply chain of an industry solution equipment manufacturer, where the merchandise is sold worldwide, but suppliers are mostly located in Asia. The preferred shipment of supply is the ocean shipment, and it takes about 5 weeks. Premium air shipment can be used to expedite delivery, but it costs substantially higher. To hedge against variability of demand and to satisfy customer service level, a certain level of safety stock is needed but inventory carrying cost can be high. Therefore, a careful fulfillment strategy is very important to balance serviceability and cost. A supply chain simulation model is developed to analyze the order fulfillment and supply planning process for the business to identify efficient supply chain strategy. The model simulates and evaluates three key performance metrics; serviceability, inventory costs and premium transportation costs, and their interactions.

The Capacitated Vehicle Routing Problem (CVRP) plays an important role in the logistics transportation sector. Determining the proper route will reduce the company's operational costs. In CVRP, a number of vehicles have a capacity limit that can serve all customers. This research completes a real case study on a bottled drinking water company where the company still uses the subjective method of the driver to determine the transportation route. Based on the conditions in the company, the selection of the best route will consider vehicle capacity and demand to determine the shortest route. The execution of this case study uses the Football Game Algorithm (FGA) which was first initiated by Fadakar Ebrahimi which proved promising and had the strongest performance in all cases. FGA is expected to be able to determine the shortest distribution route from the existing cases to reduce the distribution costs incurred. This study takes data from 4 days of delivery that served 78 customers. The average daily transportation cost savings result is 42%. This amount indicates that the FGA algorithm is effective for completing a real case study in CVRP.

Dynamic pricing strategies for efficient inventory management with auto-correlative stochastic demand forecasting using exponential smoothing method

This paper investigates the reverse logistics vehicle routing problem with a single depot, simultaneous distribution and collection of the goods by a homogeneous fleet of vehicles under the restrictions of maximum capacities and maximum distance. A mixed integer programming model is constructed To solve this problem, a mixed PSO (particle swarm optimization and simulated annealing) algorithm is designed This paper designs the coding rules of initial solution, 2-opt information exchange strategy, neighborhood solution generation strategy and cooling schedule of SA algorithm strategy. The penalty function is used in the fitness function to avoid the generation of infeasible solutions. Taking one typical instances as example, the experimental study indicates that this approach could improve the vehicle load rate and get rid of the additional total distance caused by the fluctuating vehicle load and the limited capacity. The satisfying solutions can be obtained in acceptable computational time.

The reverse logistics problem of the simultaneous distribution of commodities and the collection of reusable empty packages with a single depot and a single vehicle with limited capacity is addressed in this paper. Commodities to be distributed are loaded at the depot and the empty packages are transported back to the depot. This is called the traveling salesman problem with simultaneous delivery and pick-up (TSDP), a variant of the classical traveling salesman problem (TSP), where nodes require both delivery and pick-up. The objective is to minimize the total distance traveled by servicing of the all customers. We develop a mathematical programming model and a two-phase heuristic to solve the TSDP. In the first phase, we use an agglomerative procedure to find an initial solution. In the second phase, we develop an enhanced version of simulated annealing (SA) to search for the best solution. We tested the heuristic on standard, derived, and randomly generated data-sets and obtained encouraging results.

The paper aims to investigate the basin of attraction map of a complex Vehicle Routing Problem with random walk analysis. The Vehicle Routing Problem (VRP) is a common discrete optimization problem in field of logistics. In the case of the base VRP, the positions of one single depot and many customers (which have product demands) are given. The vehicles and their capacity limits are also fixed in the system and the objective function is the minimization of the length of the route. In the literature, many approaches have appeared to simulate the transportation demands. Most of the approaches are using some kind of metaheuristics. Solving the problems with metaheuristics requires exploring the fitness landscape of the optimization problem. The fitness landscape analysis consists of the investigation of the following elements: the set of the possible states, the fitness function and the neighborhood relationship. We use also metaheuristics are used to perform neighborhood discovery depending on the neighborhood interpretation. In this article, the following neighborhood operators are used for the basin of attraction map: 2-opt, Order Crossover (OX), Partially Matched Crossover (PMX), Cycle Crossover (CX). Based on our test results, the 2-opt and Partially Matched Crossover operators are more efficient than the Order Crossover and Cycle Crossovers.

v 1 – Introduction 1 2 Literature Review 3 2.1 Total Cost of Ownership and Lead-Time 3 2.2 Demand and Lead-Time Variability Studies 4 2.3 Resilience, Flexibility and Lengthening Supply Chain Lead-Times 7 2.4 Optimization Studies under Demand and Lead-Time Variability 8 2.5 Ties to Strategic Sourcing 9 2.6 Summary of Articles 10 2.7 Summary of Literature Search Findings 11 3 The Simulation Model 13 3.1 – Bill of Materials 13 3.2 Capacity and Daily Regeneration 14 3.3 – Backorders 14 3.4 Demand Distribution 15 3.5 Forecast Methodology 16 3.6 Lead-Time Distribution 17 3.7 Steady State 20 3.8 Safety Stock 21 3.9 Batch Size 21 3.10 Final Experimental Models 21 4 – Simulation Results and Findings 23 4.1 – Graphical Analysis 23 4.2 – Discussion of Results 26 5 Analysis of Backorders 28 5.1 Lead-Time Impact on End Products and Components 28 5.2 Demand Variance Impact on End Products Across Safety Stock Levels 28 5.3 Demand Variance Impact on Components 29

Purpose The purpose of this study is to develop an optimal production control strategy for manufacturing systems producing perishable goods under stochastic demand and machine unreliability. It aims to determine the best production rates and inventory levels that minimize total operational costs – including production, holding, shortage and disposal – while ensuring customer demand satisfaction. Additionally, the study investigates the impact of shelf-life variability and system uncertainties on operational performance, providing practical guidelines for cost-effective and resilient production planning in industries where perishability and equipment disruptions are critical concerns. Design/methodology/approach A stochastic production control model is developed for perishable goods in unreliable manufacturing systems under random demand, machine failures and limited shelf life. The model integrates production, inventory, shortage and disposal costs into a unified framework. A numerical optimization procedure is employed to determine the optimal production rates and inventory levels that minimize total operational costs while maintaining a desired service level. Sensitivity analyses are conducted to evaluate the impact of key parameters, such as shelf-life variability, demand fluctuations and shortage costs, on system performance and cost-efficiency. Findings The study demonstrates that the proposed stochastic production control model effectively minimizes total operational costs while maintaining a desired service level. Numerical results show that dynamically adjusting production based on machine status and inventory aging reduces shortages and product waste. Sensitivity analyses reveal that shelf-life duration, demand variability and shortage costs significantly influence optimal production and inventory policies. The model provides actionable insights for managing perishable goods in unreliable manufacturing systems, highlighting the importance of integrating demand uncertainty, machine failures and product perishability into production planning for cost-effective and resilient operations. Originality/value This study presents a novel stochastic production control framework that simultaneously addresses perishability, machine unreliability and stochastic demand – factors often treated separately in existing literature. By integrating production, inventory, shortage and disposal considerations into a unified model, it provides a practical tool for cost-effective and resilient production planning. The numerical optimization approach enables parameterized control policies adaptable to real-world variability. The findings offer both theoretical insights and actionable strategies for industries such as food, pharmaceuticals and biotechnology, where perishable products and system uncertainties critically impact operational efficiency and service levels.

Article history: Received 1 August 2011 Available online 10 August 2011 Distribution is an indispensable component of logistics and supply chain management. Location-Routing Problem (LRP) is an NP-hard problem that simultaneously takes into consideration location, allocation, and vehicle routing decisions to design an optimal distribution network. Multi-layer and multi-product LRP is even more complex as it deals with the decisions at multiple layers of a distribution network where multiple products are transported within and between layers of the network. This paper focuses on modeling a complicated four-layer and multi-product LRP which has not been tackled yet. The distribution network consists of plants, central depots, regional depots, and customers. In this study, the structure, assumptions, and limitations of the distribution network are defined and the mathematical optimization programming model that can be used to obtain the optimal solution is developed. Presented by a mixed-integer programming model, the LRP considers the location problem at two layers, the allocation problem at three layers, the vehicle routing problem at three layers, and a transshipment problem. The mathematical model locates central and regional depots, allocates customers to plants, central depots, and regional depots, constructs tours from each plant or open depot to customers, and constructs transshipment paths from plants to depots and from depots to other depots. Considering realistic assumptions and limitations such as producing multiple products, limited production capacity, limited depot and vehicle capacity, and limited traveling distances enables the user to capture the real world situations. © 2012 Growing Science Ltd. All rights reserved

An adaptive heuristic for the Capacitated Team Orienteering Problem

In this paper, we study an inventory system with multiple retailers under periodic review and stochastic demand. The demand is modelled as a discrete random variable. Linear holding and backorder costs as well as fixed order costs are assumed. Orders to replenish inventories can be placed at a manufacturer with a limited capacity according to a cyclic order schedule. A fixed portion of the total available capacity in a period is allocated to each retailer, who follows a modified base-stock policy to determine the order quantities. Thus, the order policy consists of four policy parameters for each retailer: the length of the review period, the first order point within a planning horizon, the individual capacity limit, and the modified base-stock level. We present an algorithm to compute the exact optimal policy parameters and two heuristics. In a numerical study, we compare the results of these approaches and derive insights into the performance of the heuristics. In addition, we introduce three different schedule types and identify the situations, in which they perform best.